Table 3 List of candidate competition indices

Distance-independent indices

  Sum of the diameters of the competitors (Steneker and Jarivis 1963)

SDBH

\(\sum_{j=1}^{n}{\mathrm{D}}_{j}\)

  Sum of the basal areas of the competitors (Steneker and Jarivis 1963)

SBA

\(\sum_{j=1}^{n}{\mathrm{BA}}_{j}\)

  Competitor to subject tree diameter (Lorimer 1983)

CSDBH

\(\frac{\sum_{j=1}^{n}{D}_{j}}{{D}_{i}}\)

  Subject tree to competitor basal area (Daniels et al. 1986)

SCBA

\(\frac{{{D}_{i}}^{2}}{n\cdot \sum_{j=1}^{n}{{D}_{j}}^{2}}\)

Distance-dependent indices

  Hegyi (1974)

Heygi

\(\sum_{j=1}^{n}\left(\frac{{D}_{j}}{{D}_{i}}\cdot \frac{1}{{\mathrm{DIST}}_{ij}}\right)\)

  Alemdag (1978)

Alem

\(\sum_{j=1}^{n}\left\{\pi \cdot {\left[\frac{{D}_{i}{\bullet \mathrm{DIST}}_{ij}}{{D}_{i}+{D}_{j}}\right]}^{2}\cdot \left[\frac{{D}_{j}/{\mathrm{DIST}}_{ij}}{\sum_{j=1}^{n}\left({D}_{j}/{\mathrm{DIST}}_{ij}\right)}\right]\right\}\)

  Johann (1982)

Joha

\(\sum_{j=1}^{n}\left(\frac{{H}_{i}}{{\mathrm{DIST}}_{ij}}\cdot \frac{{D}_{j}}{{D}_{i}}\right)\)

  Open Comparison (Hu 2010)

OP

\(\mathrm{OP}=\frac{1}{4}\sum_{j=1}^{n}{t}_{ij}\);\({t}_{ij}=\left\{\begin{array}{c}1, {\mathrm{if DIST}}_{ij}\ge {H}_{j}-{H}_{i}\\ 0, if {DIST}_{ij}<{H}_{j}-{H}_{i}\end{array}\right.\)

  Martin and Ek (1984)

MaEk

\(\sum_{j=1}^{n}\frac{{D}_{j}}{{D}_{i}}\cdot \mathrm{exp}\left[-\frac{16{\cdot \mathrm{DIST}}_{ij}}{{D}_{i}+{D}_{j}}\right]\)

  Jiang and Qiu (1994)

JiQi

\(\frac{{D}_{i}}{\frac{1}{n}\sum_{j=1}^{n}{D}_{j}}\cdot \frac{1}{n}\sum_{j=1}^{n}{\mathrm{DIST}}_{ij}\)